\textbf{113.} For values $n \geq n_0$, if the distance of the terms of the sequence $\left\{\dfrac{fn+1}{rn-2}\right\}$ from its limit is less than $0.02$, what is the smallest value of $n_0$?
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(1) $61$ \hfill (2) $62$ \hfill (3) $63$ \hfill (4) $64$
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